Heat butter and brown sugar in a 2-quart saucepan over medium heat, stirring frequently with a wooden or silicon spoon, until butter has melted and mixture is smooth. Stir in oats, flour, salt, egg, and vanilla.

Drop cookie batter by the teaspoon onto prepared baking sheets, leaving at least 2 inches between each cookie to allow them to spread.

Bake for 5 -7 minutes, watching closely to prevent them from over-baking. The lace cookies should be golden brown.

Allow to cool on the cookie sheet for 30 seconds and remove onto racks to cool completely.